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Interactive Data Exploration

A person’s muscle mass is expected to decrease with age. To explore this relationship in women, a nutritionist randomly selected 15 women from each 10-year age group, beginning with age 40 and ending with age 79. The results follow; \(X\) is age, and \(Y\) is a measure of muscle mass. Assume that first-order regression model (1.1) is appropriate.

Explore the dataset interactively:

Customize the Scatter Plot:

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First-Order Regression

Problem Statement:
A nutritionist wants to explore the relationship between muscle mass (\(Y\)) and age (\(X\)) in women. The goal is to fit a first-order regression model and analyze the relationship.

Solution and Visualization

Summary of First-Order Regression Coefficients
Estimate Std. Error t value Pr(>|t|)
(Intercept) 156.346564 5.5122625 28.36341 0
X -1.189995 0.0901973 -13.19326 0

Second-Order Regression

Problem Statement:
Extend the analysis by fitting a second-order (quadratic) regression model and evaluating its fit. Additionally, predict the mean and individual muscle mass for a 48-year-old woman.

Solution and Visualization

Summary of Second-Order Regression Coefficients
Estimate Std. Error t value Pr(>|t|)
(Intercept) 82.9357488 1.5431459 53.744593 0.0000000
x_centered -1.1839580 0.0886330 -13.357984 0.0000000
I(x_centered^2) 0.0148405 0.0083566 1.775902 0.0810869
95% Confidence and Prediction Intervals for Age 48
Type Lower Upper
Confidence Interval 96.28436 102.2249
Prediction Interval 82.91160 115.5976

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Residual Diagnostics: Normal Q-Q Plot

Visualizing Normality of Residuals:

Residuals vs. Fitted Values: